Question

: What are the coordinates of the focus of the conic section shown below?

Write your answer without using spaces.

Y^2 + 16y – 4x + 4 = 0

Answer:_________

Answer 1

Answer on Question #57358 – Math – Analytic Geometry

Question

What are the coordinates of the focus of the conic section shown below?

$$y^{2} + 16y - 4x + 4 = 0$$

Solution

$$\begin{array}{l} y^{2} + 16y - 4x + 4 = 0; \\ y^{2} + 16y + 64 - 64 - 4x + 4 = 0; \\ (y + 8)^{2} = 60 + 4x; \\ (y + 8)^{2} = 4(x + 15); \\ \end{array}$$

The vertex of the parabola has coordinates $(-15, -8)$.

As $p = 1$, it follows that the coordinates of the focus are $(-15 + 1, -8) = (-14, -8)$.

**Answer**: $(-14, -8)$.

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